HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere. HEALPix—the Hierarchical Equal Area isoLatitude Pixelization—is a versatile structure for the pixelization of data on the sphere. An associated library of computational algorithms and visualization software supports fast scientific applications executable directly on discretized spherical maps generated from very large volumes of astronomical data. Originally developed to address the data processing and analysis needs of the present generation of cosmic microwave background experiments (e.g., BOOMERANG, WMAP), HEALPix can be expanded to meet many of the profound challenges that will arise in confrontation with the observational output of future missions and experiments, including, e.g., Planck, Herschel, SAFIR, and the Beyond Einstein inflation probe. In this paper we consider the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere. We demonstrate how these are explicitly satisfied by HEALPix.

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  1. Gebhardt, Henry S. Grasshorn; Doré, Olivier: Harmonic analysis of isotropic fields on the sphere with arbitrary masks (2022)
  2. Alegría, Alfredo; Bissiri, Pier Giovanni; Cleanthous, Galatia; Porcu, Emilio; White, Philip: Multivariate isotropic random fields on spheres: nonparametric Bayesian modeling and (L^p) fast approximations (2021)
  3. Andrea Zonca, Ben Thorne, Nicoletta Krachmalnicoff, Julian Borrill: The Python Sky Model 3 software (2021) arXiv
  4. Caponera, Alessia; Marinucci, Domenico: Asymptotics for spherical functional autoregressions (2021)
  5. Goyal, Priya; Chingangbam, Pravabati: Local patch analysis for testing statistical isotropy of the Planck convergence map (2021)
  6. Jung, Gabriel; Namikawa, Toshiya; Liguori, Michele; Munshi, Dipak; Heavens, Alan: The integrated angular bispectrum of weak lensing (2021)
  7. Le Gia, Quoc T.; Li, Ming; Wang, Yu Guang: Algorithm 1018: FaVeST -- fast vector spherical harmonic transforms (2021)
  8. Marco Drago, Sergey Klimenko, Claudia Lazzaro, Edoardo Milotti, et. al: coherent WaveBurst, a pipeline for unmodeled gravitational-wave data analysis (2021) not zbMATH
  9. Nadolny, Tobias; Durrer, Ruth; Kunz, Martin; Padmanabhan, Hamsa: A new way to test the cosmological principle: measuring our peculiar velocity and the large-scale anisotropy independently (2021)
  10. Nicola, Andrina; García-García, Carlos; Alonso, David; Dunkley, Jo; Ferreira, Pedro G.; Slosar, Anže; Spergel, David N.: Cosmic shear power spectra in practice (2021)
  11. Rahman, Fazlu; Chingangbam, Pravabati; Ghosh, Tuhin: The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map (2021)
  12. Saha, Sayan; Shaikh, Shabbir; Mukherjee, Suvodip; Souradeep, Tarun; Wandelt, Benjamin D.: Bayesian estimation of our local motion from the Planck-2018 CMB temperature map (2021)
  13. Simeoni, Matthieu: Functional penalised basis pursuit on spheres (2021)
  14. Williams, Joel; McCallum, Nialh; Rotti, Aditya; Thomas, Daniel B.; Battye, Richard; Brown, Michael L.: Blind map level systematics cleaning: a quadratic estimator approach (2021)
  15. Yuan, Tianlu: The 8-parameter Fisher-Bingham distribution on the sphere (2021)
  16. Cheng, Dan; Cammarota, Valentina; Fantaye, Yabebal; Marinucci, Domenico; Schwartzman, Armin: Multiple testing of local maxima for detection of peaks on the (celestial) sphere (2020)
  17. Dargaville, Steven; Buchan, A. G.; Smedley-Stevenson, R. P.; Smith, P. N.; Pain, C. C.: Scalable angular adaptivity for Boltzmann transport (2020)
  18. Drake, Kathryn P.; Wright, Grady B.: A fast and accurate algorithm for spherical harmonic analysis on HEALPix grids with applications to the cosmic microwave background radiation (2020)
  19. Le Gia, Quoc Thong; Sloan, Ian H.; Womersley, Robert S.; Wang, Yu Guang: Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere (2020)
  20. Stough, T.; Cressie, N.; Kang, E. L.; Michalak, A. M.; Sahr, K.: Spatial analysis and visualization of global data on multi-resolution hexagonal grids (2020)

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